How to convert Torque Stabilizer to RigidBody2D?

It is a poor algorithm, but at least it's simple.

You could try these changes which preserve the existing structure - I just removed the "magnitude" conversion from the angular velocity, and fixed it to be about Vector3.forward (the Z axis), and made the AddTorque call only pass through the Z component of the calculated torque (the other components ought to be zero anyway):

 public class TorqueStabilizer2D : MonoBehaviour {
  
     public float stability = 0.3f;
     public float speed = 2.0f;
  
     void FixedUpdate () {
         Vector3 predictedUp = Quaternion.AngleAxis(
             rigidbody2D.angularVelocity * Mathf.Rad2Deg * stability / speed,
             Vector3.forward
         ) * transform.up;
  
         Vector3 torqueVector = Vector3.Cross(predictedUp, Vector3.up);
         rigidbody2D.AddTorque(torqueVector.z * speed);
     }
 }

All the messing about with vectors is very indirect though, it's essentially the same as this simpler code:

 public class TorqueStabilizer2D : MonoBehaviour {
 
     public float stability = 0.3f;
     public float speed = 2.0f;
 
     void FixedUpdate () {
         float currentAngle = Mathf.Atan2(transform.up.x, transform.up.y);
         float predictedAngle = currentAngle - rigidbody2D.angularVelocity * stability / speed;
         float torque = Mathf.Sin(predictedAngle);
         rigidbody2D.AddTorque(torque * speed);
     }
 }